function [Hleft] = updateHleft(Hleft, h1j, Opstorage1, B, BUb, h2j, A, AUb, M)
    
        if isempty(Opstorage1{1})
            for m=1:M
                Opstorage1 = zeros(size(B,1));
            end
        end
        
        if isempty(h2j{1})
            for m=1:M
                h2j{m} = zeros(size(BUb,1));
            end
        end
        
        Hleft=updateCleft(Hleft, B, BUb, [], A, AUb);
        
        if ~isempty(h1j)
            Hleft=Hleft+updateCleft([],B,BUb,h1j,A,AUb);
        end
        
        for m=1:M
            Hleft = Hleft+updateCleft(Opstorage1{m},B,BUb,h2j{m},A,AUb);
        end
end